Machines comprising a sealing station so as to produce packages after the fashion of FIG. 5 are known from the applicant. The requirements to be fulfilled by such a package comprise, on the one hand, a circumferentially extending sealed seam for hermetically sealing the interior of the package, which contains a foodstuff under vacuum or in a modified atmosphere, by sealing a cover film onto a shaped bottom film/foil. This circumferentially extending sealed seam includes a cover film that can be detached from the bottom film for the purpose of opening the package. On the other hand, an additional area outside this sealed seam is sealed in the form of a planar seal so as to provide a stable area for suspending the package. This planar seal is sealed inseparably. The planar seal can be produced by applying a pressure that is higher or lower than that used for the sealed seam. To this end, a mechanical adjustment is provided, which has to be adapted to the various combinations of films. The increased or reduced sealing pressure or a change in the sealing pressure of the planar seal must not affect the sealing pressure of the sealed seam. The mechanical adjustment is carried out by changing the amount to which the sealing surface of the sealing plate of the planar seal projects beyond or falls short of the sealed seam and is very complicated and difficult to set. The amount to which the sealing surface projects is adjusted, for example, by means of packing plates of different thicknesses.